Question

How many zeros does the expression: $1^1\times 2^2\times 3^3......{.99}^{99}\times {100}^{100}$ end in?

• A. 1050
• B. 1300
• C. 1250
• D. None of these

Answer 1

The correct option is B

1300

The number of 5's present in the expression will determine the number of 0's in the expression.
There are numbers which have single 5's as their factors, like 5,10,15.... each of these contributes that many 5's to the expression.
This gives a sum of 1050 5's (=5+10+15+ ...100).
But there are numbers like 25, 50, 75 and 100 which contribute two 5's.
So add 25+50+75+100 = 250 more to it.
It gives 1300 5's.
Hence, the answer is 1300.